Problem: $\overline{AB}$ = $2\sqrt{29}$ $\overline{AC} = {?}$ $A$ $C$ $B$ $2\sqrt{29}$ $?$ $ \sin( \angle ABC ) = \frac{2\sqrt{29} }{29}, \cos( \angle ABC ) = \frac{5\sqrt{29} }{29}, \tan( \angle ABC ) = \dfrac{2}{5}$
Answer: $\overline{AB}$ is the hypotenuse $\overline{AC}$ is opposite to $\angle ABC$ SOH CAH TOA We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH) $ \sin( \angle ABC ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\overline{AC}}{\overline{AB}}= \frac{\overline{AC}}{2\sqrt{29}} $ $ \overline{AC}=2\sqrt{29} \cdot \sin( \angle ABC ) = 2\sqrt{29} \cdot \frac{2\sqrt{29} }{29} = 4$